Production planning is the process of choosing work to be started in a manufacturing facility during some future time period so that performance is maximized. Work is usually selected from a variety of product types which may require different resources and serve different customers. Therefore, the selection must optimize customer-independent performance measures such as cycle time and customer-dependent performance measures such as on-time delivery.
The reasons for requiring advanced production planning may be unique to each manufacturing facility. For example, one facility may require advanced planning so that materials may be ordered and delivered in time for manufacture. Another facility may require advanced planning in order to make delivery commitments or predict delays in product delivery.
In order to configure a production plan which yields the best performance, the capacity, or the amount of work the facility can handle, must be modeled in some fashion, since starting work above the capacity of the facility compromises performance and brings forth no benefits. Conventional factory capacity models employ simple steady-state linear relations that include: (1) the average amount of available work time for each machine in the factory and (2) the amount of work each product requires of each machine. From the above linear relations, a given start plan is within capacity if, for each machine, the total required amount of work is: (1) less than the machine's available time, and (2) multiplied by a predetermined fraction goal utilization of the start rate.
There are several problems associated with a linear production planning program. Because of the large problem size, variables in linear programs must be expressed in non-integer quantities in order to yield good solutions. As a result, fractional start quantities may be generated which must be converted into discrete start quantities. Such forced conversion sacrifices the goodness of the solution.
Additionally, non-linear relationships cannot be modeled in a linear program. Examples of such relationships are the expected yield for a product's start quantity, and the cost of surplus and delinquency. Such non-linear relationships have been traditionally coerced into linear expressions with loss of precision.
The large problem size presents another obstacle for linear production planning programs. Even if a planning problem can be expressed in a linear program, the problem size may prohibit efficient solution via conventional linear programming techniques. This problem has not been overcome in the industry without substantial loss of optimality in the solution.
Therefore, a need has arisen for apparatus and method to formulate a production plan for a manufacturing facility that accommodates integer variables, allows non-linear expressions and provides a near optimal production plan despite the large problem size.